Although it seemed Sotirio did nothing but stand his ground, the goal was disallowed and Sydney was awarded a free kick.
That prompted a wild outburst from Babbel, who stormed towards the fourth official and let his feelings be known.
He flung his jacket to the turf in disgust and the fourth official reported the behaviour to Beath, who showed Babbel a red card.
The German kicked an advertising board before being forced to leave the SCG.
He passed by the Wanderers supporters section — the Red and Black Bloc — who cheered and applauded their coach. He gave them a thumbs up as he left the field.
Former Socceroo Andy Harper, who was commentating the game for Fox Sports, originally called Sotirio's positioning "beautiful" and "legal". His colleague Brenton Speed was also dumbfounded.
"The VAR has come up again with another howler, in many people's opinions," he added.
Football fans agreed the Wanderers were robbed, venting their outrage on social media.
While it was assumed Sotirio had been pinged for obstruction, Beath threw a spanner in the works when he explained the decision after the game, saying he was actually penalised for impacting the play while being offside.
Babbel apologised for his behaviour post-match but said: "It's just not a foul."
Melbourne Victory legend Archie Thompson disagreed with the decision and lashed the entire concept of the VAR. He was furious so many mistakes are being made with the technology and demanded it be scrapped altogether.
"The thing that's really disappointing and what's ruining our game is this," Thompson said on Fox Sports. "What baffles me is that you've actually got the footage on TV, you're reviewing it and you're still making mistakes.
"It took the sting out of what was potentially going to be a great game.
"We hear a whistle and it's like, 'Oh my God, not again, please,' almost begging and then again, it goes to VAR, stupid decision, changes the complexion of the game.
"It ruined the (Melbourne) derby last week, it's ruined the derby this week, it ruined a grand final last year.
"The football's looking better, the teams are getting better so we've got that on track, but what we're losing are these poor decisions that are ruining our game.
"I don't even want to watch it because I don't know what we're going to see.
"I think we need to scrap it because it's ruining our game."
Australian football legend Mark Bosnich said "everyone who knows football ... knows it's not a foul" when talking about the supposed block on Zullo. The ex-goalkeeper was furious and launched into a passionate spiel, saying the problem needs to be fixed or else football in Australia risks losing fans and doing irreparable damage to itself.
"We have got to suspend it (VAR) immediately in my opinion. It's becoming such a distraction, such a farce, such a talking point that it is turning people off the game," Bosnich said on Fox Sports.
"If this is not rectified, ie suspended immediately or binned altogether ... you will have 95 per cent of all your fans not going and not watching.
"It's got to stop and it's got to stop now. I'm telling you now, this has gone beyond tipping point. You are experimenting with players' livelihoods and people's livelihoods."
The VAR incident came hours after Melbourne City were angered by a missed penalty shout for Bruno Fornaroli earlier on Saturday against Central Coast. It also came after more VAR drama in Friday night's Adelaide-Newcastle game, and days of criticism which followed last week's Melbourne derby.